A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems

In this paper we introduce a new kind of Lax-Oleinik type operator with parameters associated with positive definite Lagrangian systems for both the time-periodic case and the time-independent case. On one hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution in the time-periodic case, while it was shown by Fathi and Mather that there is no such convergence of the Lax-Oleinik semigroup. On the other hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution faster than the Lax-Oleinik semigroup in the time-independent case.Comment: We give a new definition of Lax-Oleinik type operator; add some reference

Ammonium regeneration: Its contribution to phytoplankton nitrogen requirements in a eutrophic environment

Ammonium regeneration, nutrient uptake, bacterial activity and primary production were measured from March to August 1980 in Bedford Basin, Nova Scotia, Canada, a eutrophic environment. Rates of regeneration and nutrient uptake were determined using 15N isotope dilution and tracer methodology. Although primary production, nutrient uptake and ammonium regeneration were significantly intercorrelated, no relationship was detected between these parameters and heterotrophic activity. The average contribution of ammonium to total nitrogen (ammonium+nitrate) uptake was similar in the spring and in the summer (approximately 60%). On a seasonal average basis, 36% of the phytoplankton ammonium uptake could be supplied by rapid remineralization processes. In spite of the high average contribution of NH4 regeneration to phytoplankton ammonia uptake, there is indirect evidence suggesting that other NH4 sources may occasionally be important

Geodesics and the competition interface for the corner growth model

We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, out- side of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as bound- ary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions where the shape has some regularity. In a sequel to this paper the cocycles are used to prove results about semi-infinite geodesics and the competition interface

Functional Analysis of the Phycomyces carRA Gene Encoding the Enzymes Phytoene Synthase and Lycopene Cyclase

Phycomyces carRA gene encodes a protein with two domains. Domain R is characterized by red carR mutants that accumulate lycopene. Domain A is characterized by white carA mutants that do not accumulate significant amounts of carotenoids. The carRA-encoded protein was identified as the lycopene cyclase and phytoene synthase enzyme by sequence homology with other proteins. However, no direct data showing the function of this protein have been reported so far. Different Mucor circinelloides mutants altered at the phytoene synthase, the lycopene cyclase or both activities were transformed with the Phycomyces carRA gene. Fully transcribed carRA mRNA molecules were detected by Northern assays in the transformants and the correct processing of the carRA messenger was verified by RT-PCR. These results showed that Phycomyces carRA gene was correctly expressed in Mucor. Carotenoids analysis in these transformants showed the presence of ß-carotene, absent in the untransformed strains, providing functional evidence that the Phycomyces carRA gene complements the M. circinelloides mutations. Co-transformation of the carRA cDNA in E. coli with different combinations of the carotenoid structural genes from Erwinia uredovora was also performed. Newly formed carotenoids were accumulated showing that the Phycomyces CarRA protein does contain lycopene cyclase and phytoene synthase activities. The heterologous expression of the carRA gene and the functional complementation of the mentioned activities are not very efficient in E. coli. However, the simultaneous presence of both carRA and carB gene products from Phycomyces increases the efficiency of these enzymes, presumably due to an interaction mechanism

Stationary cocycles and Busemann functions for the corner growth model

We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, out- side of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as bound- ary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions where the shape has some regularity. In a sequel to this paper the cocycles are used to prove results about semi-infinite geodesics and the competition interface

Two Origins for the Gene Encoding α-Isopropylmalate Synthase in Fungi

BACKGROUND: The biosynthesis of leucine is a biochemical pathway common to prokaryotes, plants and fungi, but absent from humans and animals. The pathway is a proposed target for antimicrobial therapy. METHODOLOGY/PRINCIPAL FINDINGS: Here we identified the leuA gene encoding alpha-isopropylmalate synthase in the zygomycete fungus Phycomyces blakesleeanus using a genetic mapping approach with crosses between wild type and leucine auxotrophic strains. To confirm the function of the gene, Phycomyces leuA was used to complement the auxotrophic phenotype exhibited by mutation of the leu3+ gene of the ascomycete fungus Schizosaccharomyces pombe. Phylogenetic analysis revealed that the leuA gene in Phycomyces, other zygomycetes, and the chytrids is more closely related to homologs in plants and photosynthetic bacteria than ascomycetes or basidiomycetes, and suggests that the Dikarya have acquired the gene more recently. CONCLUSIONS/SIGNIFICANCE: The identification of leuA in Phycomyces adds to the growing body of evidence that some primary metabolic pathways or parts of them have arisen multiple times during the evolution of fungi, probably through horizontal gene transfer events